He took a swipe at the ball.
Maybe you might like to conduct a little experiment. Go outside to the nearest open space, and run 50 metres from a standing start. Try to stop your arms from moving whilst doing so.
You get my drift? Peachey was chasing a kick, ie running, from a near standing start. Just because his arms/hands were moving, does not necessarily mean he was playing at the ball. In any case, the rules only consider whether the ball was played at in determining a knock on if it was touched by the hand. Conclusive evidence has been provided that it wasn't. If the ball had touched the hands, the ref, who in this case appears to have been pretty much on the ball, would have called it as such.
I note "experts" (ie ex-players) with no connection to the losing side, on the idiot box still quibbling about this call, which was 100% correct under the rules of the game. One can only assume they were the holders of losing bets on this game, for experts of the game they surely aren't.